What do literary tourists look for when they visit the British Isles? Often it’s the quaint, old-fashioned bookshops that provide the perfect excuse to browse uninterrupted and to disconnect from the world. Until recently, the trend for barista-made coffee and high-speed Wi-Fi was considered by some in the city’s bookish crowd to be ruining London’s centuries-old tradition of disconnected browsing.

But a crop of bookshops is rebelling against frenzied online engagement and is creating environments where the real-life, internet-free book browse is the most effective way to expand your social and professional networks. And in countering the internet overload, some stores are proving to be among London’s hottest hangouts.

Leading the rebels is Libreria Books in London’s East End, which is a Wi-Fi- and coffee-free zone. It was opened in February by Rohan Silva, a former policy adviser to the former prime minister David Cameron, and co-founder of Second Home, a members’ club providing a work space for entrepreneurs.

“We’re celebrating human curation over algorithmic rhythms,” said Mr. Silva, who was spurred to open his shop after experiencing a common affliction for London’s bibliophiles — the repetitive, grating ring tones of smartphones disrupting the tranquillity of his bookshop experience. “We wanted to get people using their human intuition when they shop for books. You can get Wi-Fi anywhere now, it’s not necessary in a bookshop.”

Libreria is in the company of Tenderbooks (tenderbooks.co.uk), Buchhandlung Walther König (buchhandlung-walther-koenig.de), Lutyens & Rubinstein, (lutyensrubinstein.co.uk) and Word on the Water (facebook.com/wordonthewater), all independent book shops shunning high-speed cables and lattes. Their mantra has drawn a sophisticated, brainy crowd, but its premise is simple: In the digital age, the bookshop should be a refuge, an information overload in its own right.

“If someone gets a phone call, they leave the shop. It’s the same with the internet — people just know this isn’t the space for being online,” said Tamsin Clark, owner of Tenderbooks, which opened in 2014 in Covent Garden, a lively neighborhood packed with theaters and rare-book shops. “The thing about books is that they’re more interesting than the internet — we assume that everyone who comes here believes that.”

Creative downtime means embracing slow over fast and rejecting years of bookshop cool that’s embodied by overeager baristas and a goofy Wi-Fi-code scrawled on a chalkboard. The internet-free bookshop campaigns for the days of haughty glances over the tops of reading glasses, gentle tutting at noise, and hours spent simply considering the words on the page.

Perhaps the most serious of the bookshops is Lutyens & Rubinstein. Since 2009 its Notting Hill building has been divided between a bookshop and a literary agency — and the presence of the highbrow mood of the agency is what sets the tone for the prevailing silence of the reading room. “You wouldn’t even dare ask for the Wi-Fi code here,” a customer there said recently.

The ambience at Tenderbooks, meanwhile, tends to be a little more relaxed: “The internet can cause so much stress; we want people to come in and be more focused than they are online,” said Ms. Clark, the owner. “We’ve got a record player, we’re small and intimate. People respond really well to that. I think it’s necessary in today’s cultural climate. And because we’re in the center of London, we offer creative downtime in the heart of the city.”

Taking its name from Jorge Luis Borges’s cult 1941 classic “The Library of Babel,” a story in which every book ever written is reprinted in a 410-page edition, Libreria emphasizes a meditative experience that its owner said Wi-Fi would ruin. On Libreria’s floor-to-ceiling shelves, books are thematically curated by a rotating British who’s-who cast of the literary, political and media world, who has dreamed up book categories like “Mothers, Madonnas and Whores” and “The Sea and the Sky.” Next up as curator is the recently elected mayor of London, Sadiq Khan.

The distraction-free library ethos is actually a city tradition, from the private tranquil libraries of stately homes such as North London’s 17th-century estate Kenwood House in Hampstead Heath to the British Library’s Reading Room in King’s Cross — a place where the etiquette policy strongly discourages the presence of mobile phones entirely with tactfully placed signs. It’s in this tradition that these bookshops operate.

Mr. Silva of Libreria Books said “an old-fashioned space” is clearly appealing to book lovers. He said his shop has had twice as many customers as anticipated, with visitors from as far afield as Australia and China. Confronted with a bookshelf curated by the popular new mayor or surrounded by first editions, who wants to download a morning full of emails?